Flow structure dynamics with extreme dissipation events in homogeneous turbulence – an experimental investigation using shake-the-box and flowfit

Abstract

Since the introduction of the Richardson-Kolmogorov cascade a picture of turbulence has been created that intrinsically connects a (in general) directional down-scaling process featuring vortical flow structures with the overall energy transfer finally ending into viscous dissipation at the smallest scales of the cascade. In turbulent flows at sufficient Reynolds number intermittency of extreme dissipation events is accompanied by strong enstrophy events and both have a close relationship to the pressure Laplacian. The aim of the present investigation is to analyze the temporal dynamics of flow structures generating extreme dissipation events. Conditional ensemble averages and Lagrangian viewpoints shall complement this topological study. We present measurements of the full velocity gradient tensor and all elements of the dissipation rate based on dense fields of fluid particle trajectories in homogeneous turbulence at Re~270 and ~370 in a von Kármán flow between two counter-rotating propellers. Applying the Shake-The-Box (STB) particle tracking algorithm [1], we are able to instantaneously track up to ~100.000 particles in a measurement volume of 50 x 50 x 15 mm³. The mean inter-particle distance is lower than 7 Kolmogorov lengths. The data assimilation scheme FlowFit [2] with continuity and Navier-Stokes- constraints is used to interpolate the scattered velocity and acceleration data by continuous 3D B-Splines in a cubic grid, enabling to recover (locally) the smallest flow scales. We compute the energy dissipation rate directly by using local velocity gradient information gained by FlowFit at midpoints of particle tetrahedra in close proximity of a few Kolmogorov lengths and compare it to known inertial range approaches using two-point statistics.